Senator Day said on Saturday he believes free speech should be protected.

"Someone has to defend free speech. I think it's the basis of our society and democracy that people should be free to say what they think and allow others then to determine," he said.

"A person should not be taken to court because someone says 'I was offended by what you said'."

Indigenous politicians Ken Wyatt and Nova Peris welcomed the Prime Minister's backdown, but members of the Opposition and the Greens say they are not convinced they have seen the last attempt to change race hate laws.

"I think the Abbott Government has just put the watering down of hate speech laws in the top drawer," Opposition Leader Bill Shorten told reporters in Canberra last week.

Deputy Greens leader Adam Bandt suggested the changes are "only dead and buried for as long as the public pressure keeps up".